Taking into account Theorem 2.5 of [1]} and Remarks REF , REF  we see that, for \(s > n(\frac{1}{\theta }-\frac{1}{\max \lbrace 1,r\rbrace })\) , the
weighted Besove space \(B^{s}_{p,q}(\mathbb {R}^{n},\gamma )\)  is continuously embedded into
\(L^{\text{\rm loc}}_{\max \lbrace 1,p\rbrace }(\mathbb {R}^{n})\) ). Moreover,
\(\Vert f|B^{s}_{p,q}(\mathbb {R}^{n},\gamma )\Vert  \sim \left(\sum \limits _{k=1}^{\infty }\Vert \gamma \overline{\Delta }^{l}_{r}(2^{-k})f|L_{p}(\mathbb {R}^{n})\Vert ^{q}\right)^{\frac{1}{q}}+\Vert \gamma \Vert f|L_{r}(\cdot +I^{n})\Vert |L_{p}(\mathbb {R}^{n})\Vert \) 
